Do you have to be Jewish to believe in the Star of David and like it?

Not at all - you don't even have to be Jewish to observe the Shabbat (Sabbath) or Jewish festivals, nor to study the Torah (Jewish Bible) or even to say Jewish prayers. There have been many non-Jewish people in history who, while never formally converting to Judaism, chose to live among Jews and accept Jewish culture as their own, earning themselves the name Righteous Gentiles in the process. It's also used by some other religions, including various Christian denominations and Rastafari.